Preface to the Third Edition

1 Introduction to the Logistic Regression Model

1.1 Introduction

1.2 Fitting the Logistic Regression Model

1.3 Testing for the Significance of the Coefficients

1.4 Confidence Interval Estimation

1.5 Other Estimation Methods

1.6 Data Sets Used in Examples and Exercises

1.6.1 The ICU Study

1.6.2 The Low Birth Weight Study

1.6.3 The Global Longitudinal Study of Osteoporosis in Women

1.6.4 The Adolescent Placement Study

1.6.5 The Burn Injury Study

1.6.6 The Myopia Study

1.6.7 The NHANES Study

1.6.8 The Polypharmacy Study

Exercises

2 The Multiple Logistic Regression Model

2.1 Introduction

2.2 The Multiple Logistic Regression Model

2.3 Fitting the Multiple Logistic Regression Model

2.4 Testing for the Significance of the Model

2.5 Confidence Interval Estimation

2.6 Other Estimation Methods

Exercises

3 Interpretation of the Fitted Logistic Regression model

3.1 Introduction

3.2 Dichotomous Independent Variable

3.3 Polychotomous Independent Variable

3.4 Continuous Independent Variable

3.5 Multivariable Models

3.6 Presentation and Interpretation of the Fitted Values

3.7 A Comparison of Logistic Regression and Stratified Analysis for 2 × 2 Tables

Exercises

4 Model-Building Strategies and Methods for Logistic Regression

4.1 Introduction

4.2 Purposeful Selection of Covariates

4.2.1 Methods to Examine the Scale of a Continuous Covariate in the Logit

4.2.2 Examples of Purposeful Selection

4.3 Other Methods for Selecting Covariates

4.3.1 Stepwise Selection of Covariates

4.3.2 Best Subsets Logistic Regression

4.3.3 Selecting Covariates and Checking their Scale Using Multivariable Fractional Polynomials

4.4 Numerical Problems

Exercises

5 Assessing the Fit of the Model

5.1 Introduction

5.2 Summary Measures of Goodness of Fit

5.2.1 Pearson Chi-Square Statistic, Deviance, and Sum-of-Squares

5.2.2 The Hosmer–Lemeshow Tests

5.2.3 Classification Tables

5.2.4 Area Under the Receiver Operating Characteristic Curve

5.2.5 Other Summary Measures

5.3 Logistic Regression Diagnostics

5.4 Assessment of Fit via External Validation

5.5 Interpretation and Presentation of the Results from a Fitted Logistic Regression Model

Exercises

6 Application of Logistic Regression with Different Sampling Models

6.1 Introduction

6.2 Cohort Studies

6.3 Case-Control Studies

6.4 Fitting Logistic Regression Models to Data from Complex Sample Surveys

Exercises

7 Logistic Regression for Matched Case-Control Studies

7.1 Introduction

7.2 Methods For Assessment of Fit in a 1–*M* Matched Study

7.3 An Example Using the Logistic Regression Model in a 1–1 Matched Study

7.4 An Example Using the Logistic Regression Model in a 1–*M* Matched Study

Exercises

8 Logistic Regression Models for Multinomial and Ordinal Outcomes

8.1 The Multinomial Logistic Regression Model

8.1.1 Introduction to the Model and Estimation of Model Parameters

8.1.2 Interpreting and Assessing the Significance of the Estimated Coefficients

8.1.3 Model-Building Strategies for Multinomial Logistic Regression

8.1.4 Assessment of Fit and Diagnostic Statistics for the Multinomial Logistic Regression Model

8.2 Ordinal Logistic Regression Models

8.2.1 Introduction to the Models, Methods for Fitting, and Interpretation of Model Parameters

8.2.2 Model Building Strategies for Ordinal Logistic Regression Models

Exercises

9 Logistic Regression Models for the Analysis of Correlated Data

9.1 Introduction

9.2 Logistic Regression Models for the Analysis of Correlated Data

9.3 Estimation Methods for Correlated Data Logistic Regression Models

9.4 Interpretation of Coefficients from Logistic Regression Models for the Analysis of Correlated Data

9.4.1 Population Average Model

9.4.2 Cluster-Specific Model

9.4.3 Alternative Estimation Methods for the Cluster-Specific Model

9.4.4 Comparison of Population Average and Cluster-Specific Model

9.5 An Example of Logistic Regression Modeling with Correlated Data

9.5.1 Choice of Model for Correlated Data Analysis

9.5.2 Population Average Model

9.5.3 Cluster-Specific Model

9.5.4 Additional Points to Consider when Fitting Logistic Regression Models to Correlated Data

9.6 Assessment of Model Fit

9.6.1 Assessment of Population Average Model Fit

9.6.2 Assessment of Cluster-Specific Model Fit

9.6.3 Conclusions

Exercises

10 Special Topics

10.1 Introduction

10.2 Application of Propensity Score Methods in Logistics Regression Modeling

10.3 Exact Methods for Logistic Regression Models

10.4 Missing Data

10.5 Sample Size Issues when Fitting Logistic Regression Models

10.6 Bayesian Methods for Logistic Regression

10.6.1 The Bayesian Logistic Regression Model

10.6.2 MCMC Simulation

10.6.3 An Example of a Bayesian Analysis and Its Interpretation

10.7 Other Link Functions for Binary Regression Models

10.8 Mediation

10.8.1 Distinguishing Mediators from Confounders

10.8.2 Implications for the Interpretation of an Adjusted Logistic Regression Coefficient

10.8.3 Why Adjust for a Mediator

10.8.4 Using Logistic Regression to Assess Mediation: Assumptions

10.9 More About Statistical Interaction

10.9.1 Additive versus Multiplicative Scale–Risk Difference versus Odds Ratios

10.9.2 Estimating and Testing Additive Interaction

Exercises

References

Index